Polarised radio emission from PSR J1745-2900 has already been used to investigate the strength of the magnetic field in the Galactic Centre, close to Sagittarius A*. Here we report how persistent radio emission from this magnetar, for over four years since its discovery, has revealed large changes in the observed Faraday rotation measure, by up to 3500 rad m$^{-2}$ (a five per cent fractional change). From simultaneous analysis of the dispersion measure, we determine that these fluctuations are dominated by variations in the projected magnetic field, rather than the integrated free electron density, along the changing line of sight to the rapidly moving magnetar. From a structure function analysis of rotation measure variations, and a recent epoch of rapid change of rotation measure, we determine a minimum scale of magnetic fluctuations of size ~ 2 au at the Galactic Centre distance, inferring PSR J1745-2900 is just ~ 0.1 pc behind an additional scattering screen.
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